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0

The projection coordinates you got are wrong. We can tell that because those coordinates do not correspond to a point on the curve. We have $15 \cdot 9^{-1} \equiv 17$ and $2 \cdot 9^{-1} \equiv 13$; when we plug $x = 17$ and $y = 13$ into the original curve equation, we do not get equality, and so we know something went wrong.


3

The problem is that, imagine you sign a message $m$ using ECDSA and SHA-1 as hash algorithm. If an attacker manages to find a message $m'$ such as SHA-1$(m)$ = SHA-1$(m')$ then the computed signature for $m$ will be valid for $m'$. So the attacker can substitute $m$ for $m'$ while keeping the same signature value. The receiver who will try to validate the ...


1

That wikipedia article is about TLS, and lists separately only EC curves that have assigned numbers in TLS; for TLS all other curves fall under "arbitrary prime" or "arbitrary 2^m". OpenSSL supports for non-TLS operations including ECDSA quite a few curves not numbered for use in TLS, including the three you list. As requested, I do not comment on their ...


15

This question has many problems in the way it was asked, and clearly did not come after doing some investigation. However, since this seems to be a misconception that is spreading widely, I will relate to it. It is not true that the "crypto community" (whoever that is) believes that the NSA can break RSA. In fact, if Snowden taught us anything, it is that ...


2

I'm not sure, but I guess that two different openssl version or just builds could be done with or without support of Elliptic Curves with unsecure security levels. Furthermore your curves have very low security level, and you shouldn't use them if security is a concern (and if it's not, you probably don't need ECDSA at all). However, your assumption that ...


2

Asn1parse to the rescue. Most of the overhead is from the base64 encoding and the PEM header and footer. The raw size of the compressed form ASN1 encoding is just 44 bytes for my dummy key. And 22 of those bytes are for the 161 bits of the actual public key. $ openssl asn1parse -in compressed_public.pem -i -dump 0:d=0 hl=2 l= 42 cons: SEQUENCE ...



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